Depends on what the purpose is. It’s fine and dandy when you don’t have a lot of luggage and a lot of cushion time between LHR/LGW transfers, but considering the OP is going on vacation, he/she and his/her partner will probably be carrying a lot of luggage. I dunno, I’d rather avoid the hassle of entering the UK, collecting bags at LHR, taking the transfer bus/hired-car to LGW whose transfer times can vary depending on traffic, re-check bags, and going through security again to catch the LGW-MLE flight. Anything can go wrong between the LHR/LGW transfer like longer than expected lines, baggage not coming out fast enough, getting stuck in traffic, etc. etc. And if one considers that LGW is primarily an airport used by BA for vacationers to exotic locations, I’d try to avoid being stuck at long lines there like the plague.

Instead, I'd opt for getting into LGW directly by way of the Caribbean or Mexico (or from MCO as soon as the ban is lifted on taking BA flights between the US and UK), staying put there without the need to enter the UK and collect baggage, and smoothly transfer to the connecting flight without all the hustle and bustle.